Extrapolation-based Prediction-Correction Methods for Time-varying Convex Optimization
This addresses time-varying convex optimization for applications like signal processing and robotics, but it appears incremental as it builds on existing prediction-correction paradigms.
The paper tackles online optimization problems in signal processing and machine learning by proposing extrapolation-based prediction-correction methods, deriving an explicit bound for the tracking error.
In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on the prediction-correction paradigm, both in the primal and dual space. In particular, we leverage the typical regularized least-squares structure appearing in many signal processing problems to propose a novel and tailored prediction strategy, which we call extrapolation-based. By using tools from operator theory, we then analyze the convergence of the proposed methods as applied both to primal and dual problems, deriving an explicit bound for the tracking error, that is, the distance from the time-varying optimal solution. We further discuss the empirical performance of the algorithm when applied to signal processing, machine learning, and robotics problems.